Find the function (x, y) which satisficis laplace Prr + qyy = 0 in a rectangle 0 < x < a, 0 < y

Q: Show that the function f defined by (r, y) = (0,0) f(x, y) = { 22 + y (r, y) # (0,0) x + y

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Q: 3. f(x, y) = 5x¹ − 4x5 + 5y¹. Ans.: local minimum 0 at (0, 0), saddle at (1,0)

A: 3. Given that the function                          f(x, y)=5x4-4x5+5y4.

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

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Q: Find the maximum value of ƒ(x, y) = x²y6 for x, y ≥ 0 on the unit circle. fmax =

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Q: 2. Find the tangent plane to z = x f (t) where t = at a point (a,b) not on the y-axis. [Note: be…

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Q: Determine whether the function xy²/³ + xy ³√x⁹ + 2y³¹ 1 √3' if (x, y) = (0,0) if (x, y) = (0,0) is…

A: Let us consider a function f then f is said to be continuous at c if f(c) is defined limx→cf(x)…

Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: -3. 3) to the curve given by f(x) =

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Q: { 2xy? 9x2 + y4 (x, y) # (0,0) (x, y) = (0,0) f (x, y) ·

A: Topic = Limits and  Continuity

Q: Assume that f(r, y) is a function given by if (r, y) # (0,0), f(r, y) = 0 if (r, y) = (0, 0).

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Q: S(x,y) =-x' +2x*y-² -4y+12 ED CALC

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Q: f(x, y) = xy(3-a-y) OA. (1, В. О в. (0, 1) O C. (0,0) O P. (-3,3)

A: Given function is f(x,y)=xy(3-x-y) At first we differentiate it partially w.r.t. x and y and setting…

Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

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Q: Find the extrema of the function f (x, y) =x² + y² + x²y + 4 in the domain D={(X, Y), 1X1 <1, iyi <…

A: See the attachment

Q: y,z) = 2x^2 + 2y^2 + 4z^2 - 8z,   find all points on f(x, y, z) = 16 where the tangent plane is…

A: To find the points on f(x, y,z)=16 where the tangent plane is perpendicular to the given line…

Q: Calculate the total effect of the wind  (W(x,y))  = ) along the path which is out the line  Y = 9x…

A: Given the vector field wx,y=ycosxy,xcosxy. Consider the path y=9x, x∈0,3. Let us parametrize the…

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: c) Let f(r, y) = Vlry| Prove that f(r, y) is not differentiable at point (0, 0).

A: Given a function : f(x,y)=xy We need to show that f(x ,y) is not differentiable at (0 ,0). Let's…

Q: Evaluate ∮C (x + 3y)dx + ydy where C is the Jordan curve given by the graphs of y = e^x, y = e^−x…

A: ∮Cx+3ydx+ydy Where C:y=ex, y=e-x, y=e-1

Q: Let f(x, y, z) = x^2 + y^3 + z^5 and let u =. Find the directional derivative Du f(x, y, z).

A: The directional derivative Du​f(x,y,z) is 64/81​.Explanation:Step 1: To find the directional…

Q: Show that the function g(x, y) = is not continuous at (0,0). xy 2x² + y²¹ 0, (x, y) = (0,0) (x, y) =…

A: g(x,y)=(xy/(2x2+y2), (x, y) not equal to (0,0)               0                 ,(x, y) = (0,0)

Q: Suppose that f(1, y) = 2z² + 2y – zy Then the minimum is

A: Given: fx,y=2x4+2y4-xy We need to find the minimum value of the given function.

Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…

Q: Find an equation (x(t), y(t), z(t)) of the line that is the intersection of tangent planes at (1,…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.